2026 CCHMS P1 Q14

2026 CCHMS P1 Q14

Secondary 4
4 marks

A cake shop recorded the number of boxes of cakes sold each day over a period of 30 days.

Number of boxes sold, \(n\)Frequency
\(100\leq x<120\)4
\(120\leq x<140\)6
\(140\leq x<160\)12
\(160\leq x<180\)8
  1. Calculate an estimate of
    1. the mean daily number of boxes sold,[1]
    2. the standard deviation of the daily number of boxes sold.[1]
  2. There was an error in the recording. The shop had actually sold 30 fewer boxes of cakes each day than recorded. A correction was made to the number of boxes recorded.
    Explain how this correction will affect the mean and standard deviation calculated in (a).[2]

Solution:

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Answer:(a)(i) \(146\) boxes (ii) \(19.6\) boxes (b) Mean decreases by \(30\); standard deviation is unchanged.

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